The Scottish international goalkeeper, currently away with the national team, has recently signed an extended one-month loan deal to stay in Sheffield until the end of the season.
But his assured displays between the sticks since arriving from Goodison Park have impressed all at S6 and now Laws will be hope to sign the player in the summer - should David Moyes want to let the player leave.
He told Sky Sports: "He is doing really well for us, I'm really pleased with him and we are looking to talk to Everton about the situation between now and next season." We're only as hopeful as you can be, we are not being overly confident.
"He is their payer and they have their own ideas I'm sure, but it is something I will be discussing with the manager as soon as I can."
Meanwhile, he has denied any interest following morning reports linking The Owls with Watford's former Sheffield United striker Steve Kabba.